Classical Invariant Theory

Peter J. Olver
University of Minnesota

There has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical
developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth
of new applications, ranging from number theory to geometry, physics to computer vision. This book provides
readers with a self-contained introduction to the classical theory as well as modern developments and
applications. The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses
analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms.
A variety of innovations make this text of interest even to veterans of the subject; these include the use of
differential operators and the transform approach to the symbolic method, extension of results to arbitrary
functions, graphical methods for computing identities and Hilbert bases, complete systems of rationally and
functionally independent covariants, introduction of Lie group and Lie algebra methods, as well as a new
geometrical theory of moving frames and applications. Aimed at advanced undergraduate and graduate students the
book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and
provocative exposition.